That's the headline asserting causation based on correlation and... there actually isn't even correlation.
Quite apart from that, if car crashes decrease and suicides increase, maybe all that is really happening is that the car crash method of suicide is becoming less popular. That is, previously, some suicides were hidden within the car crash numbers. Suicide numbers will go up if the method used for a suicide makes it crushingly clear it wasn't an accident. I'll speculate that guns cause a high proportion of suicides in part for this reason.